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1.
Lutz Strüngmann 《Israel Journal of Mathematics》2006,151(1):29-51
LetR be a unital associative ring and
two classes of leftR-modules. In [St3] the notion of a (
) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses
is called a (
) pair if it is maximal with respect to the classes
and the condition Ext
R
1
(V, W)=0 for all
. In this paper we study
pairs whereR = ℤ and
is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every
pair is singly cognerated underV=L.
The author was supported by a DFG grant. 相似文献
2.
This paper examines the following question. If
and
are saturated formations then
is defined to be the class of all soluble groups whose
belong to
. In general
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing
is studied. 相似文献
3.
Götz Brunner 《Israel Journal of Mathematics》1972,12(3):306-313
In the definition ofCW-complexes, the one-point spaceP, respectively the spaceP∪* with basepoint *, play the roll of the only “building-stone”. Let
be a family of compact spaces. Then the definition of a generalizedCW-complex over
is obtained from the definition of aCW-complex by replacingP by the spaces of
and formation of the mapping cone by a slightly modified construction. LetCW
* denote the category of all pointed spaces which have the homotopy type of a generalizedCW-complex over
. If
, thenCW
* is the category of all pointedCW-spaces.CW
* is closed under the formation of direct sums and of mapping cones, cylinders and tori, and is formally characterized as
the smallest such subcategory of Top * containing the spaces W∪*,
. Following the methods of E. H. Brown, it is proved, that any half exact homotopy functor onCW
* is representable, and any cohomology theory onCW
is naturally equivalent to the cohomology theory of an Ω-spectrum; for example, the singular cohomo logy is representable
onCW
for any family
of compact spaces.
相似文献
4.
According to Grothendieck Duality Theory [RD], on each varietyV over a fieldk, there is a canonical complex of
-modules, theresidue complex
. These complexes satisfy (and are characterized by) functorial properties in the categoryV ofk-varieties. In [Ye] a complex
is constructed explicitly (when the fieldk is perfect). The main result of this paper is that the two families of complexes,
and
, which carry certain additional data (such as trace maps…), are uniquely isomorphic. As a corollary we recover Lipman’s canonical
dualizing sheaf of [Li], and we obtain formulas for residues of local cohomology classes of differential forms. 相似文献
5.
For a given centred convex bodyK of ℝ,n≥3, let
be the class of all convex bodies with the same projection body asK. The question whetherK can be expressed as a Blaschke average of two non-homothetic bodies from
is considered. Necessary and sufficient conditions onK to be Blaschke decomposable in
are given.
The paper provides also a characterization of the bodiesK such that the Blaschke indecomposable bodies in
are dense in
itself. 相似文献
6.
Yehoram Gordon 《Israel Journal of Mathematics》1981,39(1-2):141-144
LetX andY be Banach spaces. TFAE (1)X andY do not contain subspaces uniformly isomorphic to
(2) The local unconditional structure constant of the space of bounded operatorsL (X*k,Y
k) tends to infinity for every increasing sequence
and
of finite-dimensional subspaces ofX andY respectively. 相似文献
7.
Given ∈, we construct a sequence
, … of Borel sub-sigma-algebras on the unit interval with the following property. Suppose the identity functionf(x)=x is transformed by successive conditioning on
, then
, then
, Then the lim sup, with respect ton, will exceed (pointwise almost-everywhere) 1−∈ and its lim inf will be less than ∈.
The sequence of functions also will fail to converge in the
. This contrasts with the long-open conjecture that if all the
come from a finite set of sigma-algebras, then the resulting sequence of functions must converge in
.
J. L. King was partially supported by NSF grant DMS-9112595. 相似文献
8.
Let
denote the class of ergodic probability preserving transformations which are disjoint from every weakly mixing system. Let
be the class of multipliers for
, i.e. ergodic transformations whose all ergodic joinings with any element of
are also in
. Fix an ergodic rotationT, a mildly mixing actionS of a locally compact second countable groupG and an ergodic cocycle ϕ forT with values inG. The main result of the paper is a sufficient (and also necessary by [LeP] whenG is countable Abelian andS is Bernoullian) condition for the skew product build fromT, ϕ andS to be an element of
. Moreover, the self-joinings of such extensions ofT are described with an application to study semisimple extensions of rotations.
Dedicated to Hillel Furstenberg on the occasion of his retirement
The first-named author was supported in part by CRDF, grant UM1-2546-KH-03.
The second-named author was supported in part by KBN grant 1P03A 03826. 相似文献
9.
We examine the geometric theory of the weighted spaces of holomorphic functions on bounded open subsets ofC
n
,C
n
,H
v
(U) and
, by finding a lower bound for the set of weak*-exposed and weak*-strongly exposed points of the unit ball of
and give necessary and sufficient conditions for this set to be naturally homeomorphic toU. We apply these results to examine smoothness and strict convexity of
and
. We also investigate whether
is a dual space.
The second author was supported by MCYT and FEDER Project BFM2002-01423. 相似文献
10.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
11.
M. Zippin 《Israel Journal of Mathematics》1966,4(3):199-204
A basis
is constructed inc
0 such that there exists no bounded linear projection ofc
0 onto the subspace spanned by a certain subsequence
of
.
This is part of the author’s Ph.D. thesis prepared at the Hebrew University of Jerusalem under the suppervision of Professor
A. Dvoretzky and Dr. J. Lindenstrauss. The author wishes to thank Dr. Lindenstrauss for his helpful advice. 相似文献
12.
V. L. Oleînik 《Journal of Mathematical Sciences》2000,101(3):3133-3138
Let {
}, where {
} is the open unit disk on the complex plane {
}. In G, we consider analytic solutions u(t, z) ({
}, {
}) of the heat equation 2ut=uzz with initial data f(z)=u(0, z) belonging to the Fock space F, i.e., to the space of entire functions square summable with
the weight e−|z|2.Conditions on a nonnegative measure μ on G are described under which for all f ∈ F we have {
} Bibliography: 17 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 247, 1997, pp. 146–155.
Translated by S. V. Kislyakov. 相似文献
13.
J. Mossino 《Israel Journal of Mathematics》1978,30(1-2):14-50
This paper deals with some problems arising in plasma physics. The typical example is the following:
where
is the (neither local, nor monotone, nor continuous) operator:
. Using a quasi-variational approach, we prove the existence of minimal and maximal solutions for a weak form of this problem,
involving a multi-valued operator β. Various generalizations are treated.
相似文献
14.
Let K be a field and
a non-trivial valuation ring of K withm as its maximal ideal. Denote by
and
the rings of polynomials f∈K[X] and rational functions f∈K(X) resp. such that
. We prove that for one variable X we have
if and only if the completion of (K,
) is locally compact or algebraically closed. In the second case—i.e. if K is dense in the algebraic closure of (K,
)—we even get
for any number of variables X=(X1,...,Xn).
This work contains parts of the second author's thesis [Ri] written under the supervision of the first author. 相似文献
15.
Zoé Chatzidakis 《Israel Journal of Mathematics》1986,55(2):173-183
LetK be a hilbertian field,G(K) its absolute Galois group. IfK is countable, then for a.a.
inG(K)
e
,
and there is no intermediate field
with
. Let
∈G(K)
e
. Then for a.a.
in
. 相似文献
16.
We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. 相似文献
17.
For an idealJ on an infinite setX with add(J)=κ, let
be the smallest size of any subfamilyY ofJ with the property that any member ofJ can be covered by less than κ members ofY. We study the value of
forA in
, where
denotes the smallest [δ]<θ ideal onP
κ(λ). We also discuss the problem of whether there exists a setA such that
, or even
.
Some of the material in this paper originally appeared as part of the author's doctoral dissertation completed at the Université
de Caen, 1998.
Partially supported by the Israel Science Foundation. Publication 813. 相似文献
18.
Jong Taek Cho 《Israel Journal of Mathematics》1999,109(1):299-318
N. Tanaka ([10]) defined the canonical affine connection on a nondegenerate integrable CR manifold. In the present paper,
we introduce a new class of contact Riemannian manifolds satisfying (C) (
for any unit
-geodesic (
, where
is the generalized Tanaka connection. In particular, when the associated CR structure of a given contact Riemannian manifold
is integrable we have a structure theorem and find examples which are neither Sasakian nor locally symmetric but satisfy the
condition (C).
This work was supported in part by BSRI 98-1425. 相似文献
19.
We show that for a
-action Ψ being the Kronecker sum of a symbolic strictly ergodic
-actionT and a Chacon
-actionS, the rank (covering number) of Ψ is the same as that forT. Using this result we construct, for a given natural numberr≥2 and a real numberb∈(0,1) withr\b≥1, a
-action with rankr, covering numberb and a simple spectrum. On the other hand, for any positive integersr, m with 1≤m≤r≤∞ we construct a
-action with rankr and spectral multiplicitym. 相似文献
20.
V. Hinich 《Israel Journal of Mathematics》1991,73(3):297-308
Let
be a nilpotent orbit of the adjoint action of a complex connected semi-simple Lie group on its Lie algebra. We prove that
the normalization of the closure of
is Gorenstein and has rational singularities. 相似文献